To account for the entire SED from Tycho, we calculate synchrotron radiation of electrons and \(\gamma \) -ray radiation resulting from leptonic and hadronic interactions. The synchrotron emission is calculated following [1]}.
Care must be exercised to properly account for magnetic field fluctuations in calculating the synchrotron emissivity function. The standard calculation, although not applicable
to the turbulent magnetic field, assumes by default a delta function for the probability distribution of local magnetic-field amplitudes. For the turbulent magnetic-field the amplitudes distribution is dispersed compared to the standard case. Its exact form is unknown. In the literature, however, one finds modified emissivities for exponential [2]} and power-law [3]} distributions.
In this work we use the Gaussian distribution of magnetic-field amplitudes and the corresponding synchrotron emissivity function [4]}.
Given the low gas density, non-thermal bremsstrahlung [1]} yields too low a flux for it to be relevant, and so leptonic gamma-ray emission is solely provided by inverse Compton scattering, for which we consider the microwave background as the target photon field [1]}, [7]}.
Tycho shows evidence for infrared emission [8]}. Its contribution for the overall inverse-Compton spectrum,
investigated by [9]} was, however, found to be negligible.
Hadronic \(\gamma \) -rays are the result of decays of neutral pions and other secondaries produced in interactions of cosmic rays with nuclei of the ISM. To calculate its spectrum we follow the method from [10]}.
